Does anybody know the (computational) fastest way to calculate the internal angles (minimal internal angle) of a cube, result of a trilinear interpolation between 8 points, in 3D space, of course.

Aren't all the cube internal angles 90 degrees?...
I guess you meant a hexa rather than a cube.
A straightforward way is computing angles from scalar product of vectors. Doing this for all the combinations you need, you can find the minimum angle.
Not sure this is the fastest way, and whether it is what you were asking.